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<div class="title">AutoDiffScalar.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2009 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_AUTODIFF_SCALAR_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_AUTODIFF_SCALAR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B&gt;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">struct </span>make_coherent_impl {</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(A&amp;, B&amp;) {}</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;};</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160; </div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">// resize a to match b is a.size()==0, and conversely.</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B&gt;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keywordtype">void</span> make_coherent(<span class="keyword">const</span> A&amp; a, <span class="keyword">const</span> B&amp;b)</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;{</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  make_coherent_impl&lt;A,B&gt;::run(a.const_cast_derived(), b.const_cast_derived());</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;}</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerivativeType, <span class="keywordtype">bool</span> Enable&gt; <span class="keyword">struct </span>auto_diff_special_op;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerivativeType&gt; <span class="keyword">class </span>AutoDiffScalar;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> NewDerType&gt;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="keyword">inline</span> AutoDiffScalar&lt;NewDerType&gt; MakeAutoDiffScalar(<span class="keyword">const</span> <span class="keyword">typename</span> NewDerType::Scalar&amp; value, <span class="keyword">const</span> NewDerType &amp;der) {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  <span class="keywordflow">return</span> AutoDiffScalar&lt;NewDerType&gt;(value,der);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;}</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerivativeType&gt;</div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classEigen_1_1AutoDiffScalar.html">   69</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar</a></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  : <span class="keyword">public</span> internal::auto_diff_special_op</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            &lt;DerivativeType, !internal::is_same&lt;typename internal::traits&lt;internal::remove_all_t&lt;DerivativeType&gt;&gt;::Scalar,</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                                          typename NumTraits&lt;typename internal::traits&lt;internal::remove_all_t&lt;DerivativeType&gt;&gt;::Scalar&gt;::Real&gt;::value&gt;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;{</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keyword">typedef</span> internal::auto_diff_special_op</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            &lt;DerivativeType, !internal::is_same&lt;typename internal::traits&lt;internal::remove_all_t&lt;DerivativeType&gt;&gt;::Scalar,</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                       <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;typename internal::traits&lt;internal::remove_all_t&lt;DerivativeType&gt;</a>&gt;::Scalar&gt;::Real&gt;::value&gt; Base;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keyword">typedef</span> internal::remove_all_t&lt;DerivativeType&gt; DerType;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits&lt;DerType&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> Real;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keyword">using</span> Base::operator+;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keyword">using</span> Base::operator*;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">   86</a></span>&#160;    <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>() {}</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classEigen_1_1AutoDiffScalar.html#ac495df4f841747d994c15970804b0f55">   90</a></span>&#160;    <a class="code" href="classEigen_1_1AutoDiffScalar.html#ac495df4f841747d994c15970804b0f55">AutoDiffScalar</a>(<span class="keyword">const</span> Scalar&amp; value, <span class="keywordtype">int</span> nbDer, <span class="keywordtype">int</span> derNumber)</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;      : m_value(value), m_derivatives(DerType::Zero(nbDer))</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    {</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;      m_derivatives.coeffRef(derNumber) = Scalar(1);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    }</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="classEigen_1_1AutoDiffScalar.html#adbf812d694d82049f27b55fbd6c1fb50">   98</a></span>&#160;    <span class="comment">/*explicit*/</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#adbf812d694d82049f27b55fbd6c1fb50">AutoDiffScalar</a>(<span class="keyword">const</span> Real&amp; value)</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;      : m_value(value)</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    {</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;      <span class="keywordflow">if</span>(m_derivatives.size()&gt;0)</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        m_derivatives.setZero();</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    }</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classEigen_1_1AutoDiffScalar.html#ae6483e33249241b62b9f2506faaf8bbf">  106</a></span>&#160;    <a class="code" href="classEigen_1_1AutoDiffScalar.html#ae6483e33249241b62b9f2506faaf8bbf">AutoDiffScalar</a>(<span class="keyword">const</span> Scalar&amp; value, <span class="keyword">const</span> DerType&amp; der)</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;      : m_value(value), m_derivatives(der)</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    {}</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;OtherDerType&gt;</a>&amp; other</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;#ifndef EIGEN_PARSED_BY_DOXYGEN</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    , std::enable_if_t&lt;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            internal::is_same&lt;Scalar, <span class="keyword">typename</span> internal::traits&lt;internal::remove_all_t&lt;OtherDerType&gt;&gt;::Scalar&gt;::value</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        &amp;&amp;  internal::is_convertible&lt;OtherDerType,DerType&gt;::value , <span class="keywordtype">void</span>*&gt; = 0</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;#endif</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    )</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;      : m_value(other.value()), m_derivatives(other.derivatives())</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    {}</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keyword">friend</span>  std::ostream &amp; operator &lt;&lt; (std::ostream &amp; s, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; a)</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    {</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;      <span class="keywordflow">return</span> s &lt;&lt; a.value();</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; other)</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;      : m_value(other.value()), m_derivatives(other.derivatives())</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    {}</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      m_value = other.value();</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;      m_derivatives = other.derivatives();</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    }</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; other)</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    {</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;      m_value = other.value();</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;      m_derivatives = other.derivatives();</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    }</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    {</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;      m_value = other;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;      <span class="keywordflow">if</span>(m_derivatives.size()&gt;0)</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        m_derivatives.setZero();</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    }</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">//     inline operator const Scalar&amp; () const { return m_value; }</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">//     inline operator Scalar&amp; () { return m_value; }</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> Scalar&amp; value()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_value; }</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="keyword">inline</span> Scalar&amp; value() { <span class="keywordflow">return</span> m_value; }</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> DerType&amp; derivatives()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_derivatives; }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keyword">inline</span> DerType&amp; derivatives() { <span class="keywordflow">return</span> m_derivatives; }</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt; (<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &lt;  other; }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt;=(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &lt;= other; }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt; (<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &gt;  other; }</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt;=(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &gt;= other; }</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value == other; }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator!=(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value != other; }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt; (<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a &lt;  b.value(); }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt;=(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a &lt;= b.value(); }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt; (<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a &gt;  b.value(); }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt;=(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a &gt;= b.value(); }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a == b.value(); }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator!=(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b) { <span class="keywordflow">return</span> a != b.value(); }</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160; </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt; (<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &lt;  b.value(); }</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&lt;=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &lt;= b.value(); }</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt; (<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &gt;  b.value(); }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator&gt;=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value &gt;= b.value(); }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value == b.value(); }</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt; <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator!=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; b)<span class="keyword"> const  </span>{ <span class="keywordflow">return</span> m_value != b.value(); }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;DerType&amp;&gt; operator+(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;DerType&amp;&gt;(m_value + other, m_derivatives);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    }</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160; </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> AutoDiffScalar&lt;DerType&amp;&gt; operator+(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b)</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    {</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;DerType&amp;&gt;(a + b.value(), b.derivatives());</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    }</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="comment">//     inline const AutoDiffScalar&lt;DerType&amp;&gt; operator+(const Real&amp; other) const</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;DerType&amp;&gt;(m_value + other, m_derivatives);</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="comment">//     friend inline const AutoDiffScalar&lt;DerType&amp;&gt; operator+(const Real&amp; a, const AutoDiffScalar&amp; b)</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;DerType&amp;&gt;(a + b.value(), b.derivatives());</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator+=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    {</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;      value() += other;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;CwiseBinaryOp&lt;internal::scalar_sum_op&lt;Scalar&gt;,<span class="keyword">const</span> DerType,<span class="keyword">const</span> internal::remove_all_t&lt;OtherDerType&gt;&gt; &gt;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    operator+(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;      internal::make_coherent(m_derivatives, other.derivatives());</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;CwiseBinaryOp&lt;internal::scalar_sum_op&lt;Scalar&gt;,<span class="keyword">const</span> DerType,<span class="keyword">const</span> internal::remove_all_t&lt;OtherDerType&gt;&gt; &gt;(</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;        m_value + other.value(),</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        m_derivatives + other.derivatives());</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    }</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    operator+=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    {</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;      (*this) = (*this) + other;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    }</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160; </div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;DerType&amp;&gt; operator-(<span class="keyword">const</span> Scalar&amp; b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;DerType&amp;&gt;(m_value - b, m_derivatives);</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    }</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> AutoDiffScalar&lt;CwiseUnaryOp&lt;internal::scalar_opposite_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType&gt; &gt;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    operator-(<span class="keyword">const</span> Scalar&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; b)</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    {</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;CwiseUnaryOp&lt;internal::scalar_opposite_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType&gt; &gt;</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            (a - b.value(), -b.derivatives());</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    }</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator-=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    {</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;      value() -= other;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    }</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;CwiseBinaryOp&lt;internal::scalar_difference_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType,<span class="keyword">const</span> internal::remove_all_t&lt;OtherDerType&gt;&gt; &gt;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    operator-(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;      internal::make_coherent(m_derivatives, other.derivatives());</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;CwiseBinaryOp&lt;internal::scalar_difference_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType,<span class="keyword">const</span> internal::remove_all_t&lt;OtherDerType&gt;&gt; &gt;(</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        m_value - other.value(),</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        m_derivatives - other.derivatives());</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    }</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    operator-=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    {</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;      *<span class="keyword">this</span> = *<span class="keyword">this</span> - other;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    }</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; </div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;CwiseUnaryOp&lt;internal::scalar_opposite_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType&gt; &gt;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    operator-()<span class="keyword"> const</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;      <span class="keywordflow">return</span> AutoDiffScalar&lt;CwiseUnaryOp&lt;internal::scalar_opposite_op&lt;Scalar&gt;, <span class="keyword">const</span> DerType&gt; &gt;(</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        -m_value,</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        -m_derivatives);</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    }</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&lt;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) &gt;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    operator*(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(m_value * other, m_derivatives * other);</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    }</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160; </div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&lt;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) &gt;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    operator*(<span class="keyword">const</span> Scalar&amp; other, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; a)</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    {</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(a.value() * other, a.derivatives() * other);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    }</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;<span class="comment">//     inline const AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="comment">//     operator*(const Real&amp; other) const</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;(</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="comment">//         m_value * other,</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;<span class="comment">//         (m_derivatives * other));</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="comment">//     friend inline const AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;</span></div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="comment">//     operator*(const Real&amp; other, const AutoDiffScalar&amp; a)</span></div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;(</span></div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="comment">//         a.value() * other,</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="comment">//         a.derivatives() * other);</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&lt;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) &gt;</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;    operator/(<span class="keyword">const</span> Scalar&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    }</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160; </div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    <span class="keyword">friend</span> <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&lt;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) &gt;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    operator/(<span class="keyword">const</span> Scalar&amp; other, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; a)</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    {</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value()*a.value())));</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    }</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160; </div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="comment">//     inline const AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;</span></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="comment">//     operator/(const Real&amp; other) const</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;(</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;<span class="comment">//         m_value / other,</span></div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;<span class="comment">//         (m_derivatives * (Real(1)/other)));</span></div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="comment">//     friend inline const AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="comment">//     operator/(const Real&amp; other, const AutoDiffScalar&amp; a)</span></div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="comment">//     {</span></div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="comment">//       return AutoDiffScalar&lt;typename CwiseUnaryOp&lt;internal::scalar_multiple_op&lt;Real&gt;, DerType&gt;::Type &gt;(</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;<span class="comment">//         other / a.value(),</span></div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;<span class="comment">//         a.derivatives() * (-Real(1)/other));</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="comment">//     }</span></div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&lt;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;        CwiseBinaryOp&lt;internal::scalar_difference_op&lt;Scalar&gt; EIGEN_COMMA</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;          <span class="keyword">const</span> EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;          <span class="keyword">const</span> EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t&lt;OtherDerType&gt;,Scalar,product) &gt;,Scalar,product) &gt;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;    operator/(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;      internal::make_coherent(m_derivatives, other.derivatives());</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        m_value / other.value(),</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;          ((m_derivatives * other.value()) - (other.derivatives() * m_value))</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        * (Scalar(1)/(other.value()*other.value())));</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    }</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160; </div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    <span class="keyword">inline</span> AutoDiffScalar&lt;CwiseBinaryOp&lt;internal::scalar_sum_op&lt;Scalar&gt;,</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;        <span class="keyword">const</span> EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;        <span class="keyword">const</span> EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t&lt;OtherDerType&gt;,Scalar,product) &gt; &gt;</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    operator*(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      internal::make_coherent(m_derivatives, other.derivatives());</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      <span class="keywordflow">return</span> MakeAutoDiffScalar(</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;        m_value * other.value(),</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        (m_derivatives * other.value()) + (other.derivatives() * m_value));</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    }</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator*=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;    {</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      *<span class="keyword">this</span> = *<span class="keyword">this</span> * other;</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    }</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160; </div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator*=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    {</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;      *<span class="keyword">this</span> = *<span class="keyword">this</span> * other;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    }</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160; </div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator/=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;    {</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;      *<span class="keyword">this</span> = *<span class="keyword">this</span> / other;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    }</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160; </div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> OtherDerType&gt;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">AutoDiffScalar</a>&amp; operator/=(<span class="keyword">const</span> AutoDiffScalar&lt;OtherDerType&gt;&amp; other)</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;    {</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;      *<span class="keyword">this</span> = *<span class="keyword">this</span> / other;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    }</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160; </div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    Scalar m_value;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    DerType m_derivatives;</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160; </div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;};</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160; </div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerivativeType&gt;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;<span class="keyword">struct </span>auto_diff_special_op&lt;DerivativeType, true&gt;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;<span class="comment">//   : auto_diff_scalar_op&lt;DerivativeType, typename NumTraits&lt;Scalar&gt;::Real,</span></div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;<span class="comment">//                            is_same&lt;Scalar,typename NumTraits&lt;Scalar&gt;::Real&gt;::value&gt;</span></div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;{</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;  <span class="keyword">typedef</span> remove_all_t&lt;DerivativeType&gt; DerType;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> traits&lt;DerType&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Scalar&gt;::Real Real;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160; </div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;<span class="comment">//   typedef auto_diff_scalar_op&lt;DerivativeType, typename NumTraits&lt;Scalar&gt;::Real,</span></div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;<span class="comment">//                            is_same&lt;Scalar,typename NumTraits&lt;Scalar&gt;::Real&gt;::value&gt; Base;</span></div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160; </div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;<span class="comment">//   using Base::operator+;</span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="comment">//   using Base::operator+=;</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="comment">//   using Base::operator-;</span></div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;<span class="comment">//   using Base::operator-=;</span></div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;<span class="comment">//   using Base::operator*;</span></div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;<span class="comment">//   using Base::operator*=;</span></div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160; </div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  <span class="keyword">const</span> AutoDiffScalar&lt;DerivativeType&gt;&amp; derived()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>AutoDiffScalar&lt;DerivativeType&gt;*<span class="keyword">&gt;</span>(<span class="keyword">this</span>); }</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  AutoDiffScalar&lt;DerivativeType&gt;&amp; derived() { <span class="keywordflow">return</span> *<span class="keyword">static_cast&lt;</span>AutoDiffScalar&lt;DerivativeType&gt;*<span class="keyword">&gt;</span>(<span class="keyword">this</span>); }</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160; </div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  <span class="keyword">inline</span> AutoDiffScalar&lt;DerType&amp;&gt; operator+(<span class="keyword">const</span> Real&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    <span class="keywordflow">return</span> AutoDiffScalar&lt;DerType&amp;&gt;(derived().value() + other, derived().derivatives());</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  }</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160; </div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;  <span class="keyword">friend</span> <span class="keyword">inline</span> AutoDiffScalar&lt;DerType&amp;&gt; operator+(<span class="keyword">const</span> Real&amp; a, <span class="keyword">const</span> AutoDiffScalar&lt;DerivativeType&gt;&amp; b)</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  {</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    <span class="keywordflow">return</span> AutoDiffScalar&lt;DerType&amp;&gt;(a + b.value(), b.derivatives());</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;  }</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160; </div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  <span class="keyword">inline</span> AutoDiffScalar&lt;DerivativeType&gt;&amp; operator+=(<span class="keyword">const</span> Real&amp; other)</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  {</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;    derived().value() += other;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;    <span class="keywordflow">return</span> derived();</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  }</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160; </div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160; </div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  <span class="keyword">inline</span> AutoDiffScalar&lt;typename CwiseUnaryOp&lt;bind2nd_op&lt;scalar_product_op&lt;Scalar,Real&gt; &gt;, DerType&gt;::Type &gt;</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  <a class="codeRef" href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">operator*</a>(<span class="keyword">const</span> Real&amp; other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;    <span class="keywordflow">return</span> AutoDiffScalar&lt;typename CwiseUnaryOp&lt;bind2nd_op&lt;scalar_product_op&lt;Scalar,Real&gt; &gt;, DerType&gt;::Type &gt;(</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;      derived().value() * other,</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;      derived().derivatives() * other);</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  }</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160; </div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;  <span class="keyword">friend</span> <span class="keyword">inline</span> AutoDiffScalar&lt;typename CwiseUnaryOp&lt;bind1st_op&lt;scalar_product_op&lt;Real,Scalar&gt; &gt;, DerType&gt;::Type &gt;</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  <a class="codeRef" href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">operator*</a>(<span class="keyword">const</span> Real&amp; other, <span class="keyword">const</span> AutoDiffScalar&lt;DerivativeType&gt;&amp; a)</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  {</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    <span class="keywordflow">return</span> AutoDiffScalar&lt;typename CwiseUnaryOp&lt;bind1st_op&lt;scalar_product_op&lt;Real,Scalar&gt; &gt;, DerType&gt;::Type &gt;(</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;      a.value() * other,</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;      a.derivatives() * other);</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  }</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160; </div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <span class="keyword">inline</span> AutoDiffScalar&lt;DerivativeType&gt;&amp; operator*=(<span class="keyword">const</span> Scalar&amp; other)</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  {</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    *<span class="keyword">this</span> = *<span class="keyword">this</span> * other;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    <span class="keywordflow">return</span> derived();</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  }</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;};</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160; </div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerivativeType&gt;</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;<span class="keyword">struct </span>auto_diff_special_op&lt;DerivativeType, false&gt;</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;{</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  <span class="keywordtype">void</span> <a class="codeRef" href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">operator*</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;  <span class="keywordtype">void</span> operator-() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;  <span class="keywordtype">void</span> operator+() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;};</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> BinOp, <span class="keyword">typename</span> A, <span class="keyword">typename</span> B, <span class="keyword">typename</span> RefType&gt;</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keywordtype">void</span> make_coherent_expression(CwiseBinaryOp&lt;BinOp,A,B&gt; xpr, <span class="keyword">const</span> RefType &amp;ref)</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;{</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  make_coherent(xpr.const_cast_derived().lhs(), ref);</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  make_coherent(xpr.const_cast_derived().rhs(), ref);</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;}</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160; </div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> UnaryOp, <span class="keyword">typename</span> A, <span class="keyword">typename</span> RefType&gt;</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;<span class="keywordtype">void</span> make_coherent_expression(<span class="keyword">const</span> CwiseUnaryOp&lt;UnaryOp,A&gt; &amp;xpr, <span class="keyword">const</span> RefType &amp;ref)</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;{</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;  make_coherent(xpr.nestedExpression().const_cast_derived(), ref);</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;}</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160; </div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;<span class="comment">// needed for compilation only</span></div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> UnaryOp, <span class="keyword">typename</span> A, <span class="keyword">typename</span> RefType&gt;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;<span class="keywordtype">void</span> make_coherent_expression(<span class="keyword">const</span> CwiseNullaryOp&lt;UnaryOp,A&gt; &amp;, <span class="keyword">const</span> RefType &amp;)</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;{}</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160; </div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> A_Scalar, <span class="keywordtype">int</span> A_Rows, <span class="keywordtype">int</span> A_Cols, <span class="keywordtype">int</span> A_Options, <span class="keywordtype">int</span> A_MaxRows, <span class="keywordtype">int</span> A_MaxCols, <span class="keyword">typename</span> B&gt;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="keyword">struct </span>make_coherent_impl&lt;Matrix&lt;A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols&gt;, B&gt; {</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols&gt; A;</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(A&amp; a, B&amp; b) {</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="keywordflow">if</span>((A_Rows==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || A_Cols==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>) &amp;&amp; (a.size()==0))</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    {</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;      a.resize(b.size());</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;      a.setZero();</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    }</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (B::SizeAtCompileTime==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp; a.size()!=0 &amp;&amp; b.size()==0)</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    {</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;      make_coherent_expression(b,a);</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    }</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  }</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;};</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160; </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B_Scalar, <span class="keywordtype">int</span> B_Rows, <span class="keywordtype">int</span> B_Cols, <span class="keywordtype">int</span> B_Options, <span class="keywordtype">int</span> B_MaxRows, <span class="keywordtype">int</span> B_MaxCols&gt;</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;<span class="keyword">struct </span>make_coherent_impl&lt;A, Matrix&lt;B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols&gt; &gt; {</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols&gt; B;</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(A&amp; a, B&amp; b) {</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    <span class="keywordflow">if</span>((B_Rows==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || B_Cols==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>) &amp;&amp; (b.size()==0))</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    {</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;      b.resize(a.size());</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;      b.setZero();</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;    }</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (A::SizeAtCompileTime==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> &amp;&amp; b.size()!=0 &amp;&amp; a.size()==0)</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;    {</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;      make_coherent_expression(a,b);</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;    }</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  }</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;};</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160; </div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> A_Scalar, <span class="keywordtype">int</span> A_Rows, <span class="keywordtype">int</span> A_Cols, <span class="keywordtype">int</span> A_Options, <span class="keywordtype">int</span> A_MaxRows, <span class="keywordtype">int</span> A_MaxCols,</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;         <span class="keyword">typename</span> B_Scalar, <span class="keywordtype">int</span> B_Rows, <span class="keywordtype">int</span> B_Cols, <span class="keywordtype">int</span> B_Options, <span class="keywordtype">int</span> B_MaxRows, <span class="keywordtype">int</span> B_MaxCols&gt;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;<span class="keyword">struct </span>make_coherent_impl&lt;Matrix&lt;A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols&gt;,</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;                          Matrix&lt;B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols&gt; &gt; {</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols&gt; A;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols&gt; B;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(A&amp; a, B&amp; b) {</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;    <span class="keywordflow">if</span>((A_Rows==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || A_Cols==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>) &amp;&amp; (a.size()==0))</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    {</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;      a.resize(b.size());</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;      a.setZero();</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;    }</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span>((B_Rows==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || B_Cols==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>) &amp;&amp; (b.size()==0))</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;    {</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;      b.resize(a.size());</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;      b.setZero();</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;    }</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  }</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;};</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160; </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160; </div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> BinOp&gt;</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;AutoDiffScalar&lt;DerType&gt;,typename DerType::Scalar,BinOp&gt;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;{</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;  <span class="keyword">typedef</span> AutoDiffScalar&lt;DerType&gt; ReturnType;</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;};</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160; </div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> BinOp&gt;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;typename DerType::Scalar,AutoDiffScalar&lt;DerType&gt;, BinOp&gt;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;{</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;  <span class="keyword">typedef</span> AutoDiffScalar&lt;DerType&gt; ReturnType;</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;};</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160; </div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160; </div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;<span class="comment">// The following is an attempt to let Eigen&#39;s known about expression template, but that&#39;s more tricky!</span></div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160; </div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;<span class="comment">// template&lt;typename DerType, typename BinOp&gt;</span></div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;<span class="comment">// struct ScalarBinaryOpTraits&lt;AutoDiffScalar&lt;DerType&gt;,AutoDiffScalar&lt;DerType&gt;, BinOp&gt;</span></div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;<span class="comment">// {</span></div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;<span class="comment">//   enum { Defined = 1 };</span></div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;<span class="comment">//   typedef AutoDiffScalar&lt;typename DerType::PlainObject&gt; ReturnType;</span></div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;<span class="comment">// };</span></div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;<span class="comment">// template&lt;typename DerType1,typename DerType2, typename BinOp&gt;</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;<span class="comment">// struct ScalarBinaryOpTraits&lt;AutoDiffScalar&lt;DerType1&gt;,AutoDiffScalar&lt;DerType2&gt;, BinOp&gt;</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;<span class="comment">// {</span></div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;<span class="comment">//   enum { Defined = 1 };//internal::is_same&lt;typename DerType1::Scalar,typename DerType2::Scalar&gt;::value };</span></div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;<span class="comment">//   typedef AutoDiffScalar&lt;typename DerType1::PlainObject&gt; ReturnType;</span></div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;<span class="comment">// };</span></div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160; </div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;<span class="preprocessor">#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \</span></div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;<span class="preprocessor">  template&lt;typename DerType&gt; \</span></div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;<span class="preprocessor">  inline Eigen::AutoDiffScalar&lt; \</span></div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;<span class="preprocessor">  EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Eigen::internal::remove_all_t&lt;DerType&gt;, typename Eigen::internal::traits&lt;Eigen::internal::remove_all_t&lt;DerType&gt;&gt;::Scalar, product) &gt; \</span></div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;<span class="preprocessor">  FUNC(const Eigen::AutoDiffScalar&lt;DerType&gt;&amp; x) { \</span></div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;<span class="preprocessor">    using namespace Eigen; \</span></div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="preprocessor">    typedef typename Eigen::internal::traits&lt;Eigen::internal::remove_all_t&lt;DerType&gt;&gt;::Scalar Scalar; \</span></div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;<span class="preprocessor">    EIGEN_UNUSED_VARIABLE(sizeof(Scalar)); \</span></div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;<span class="preprocessor">    CODE; \</span></div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;<span class="preprocessor">  }</span></div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160; </div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="keyword">struct </span>CleanedUpDerType {</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;  <span class="keyword">typedef</span> AutoDiffScalar&lt;typename Eigen::internal::remove_all_t&lt;DerType&gt;::PlainObject&gt; type;</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;};</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160; </div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;<span class="keyword">inline</span> <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; <a class="codeRef" href="../namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">conj</a>(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x)  { <span class="keywordflow">return</span> x; }</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;<span class="keyword">inline</span> <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; <a class="codeRef" href="../namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">real</a>(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x)  { <span class="keywordflow">return</span> x; }</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> DerType::Scalar <a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp;)    { <span class="keywordflow">return</span> 0.; }</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (min)(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x, <span class="keyword">const</span> T&amp; y) {</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type ADS;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  <span class="keywordflow">return</span> (x &lt;= y ? ADS(x) : ADS(y));</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;}</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (max)(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x, <span class="keyword">const</span> T&amp; y) {</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type ADS;</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  <span class="keywordflow">return</span> (x &gt;= y ? ADS(x) : ADS(y));</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;}</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (min)(<span class="keyword">const</span> T&amp; x, <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; y) {</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type ADS;</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  <span class="keywordflow">return</span> (x &lt; y ? ADS(x) : ADS(y));</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;}</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (max)(<span class="keyword">const</span> T&amp; x, <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; y) {</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type ADS;</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;  <span class="keywordflow">return</span> (x &gt; y ? ADS(x) : ADS(y));</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;}</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (min)(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x, <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; y) {</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  <span class="keywordflow">return</span> (x.value() &lt; y.value() ? x : y);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;}</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerType&gt;</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> CleanedUpDerType&lt;DerType&gt;::type (max)(<span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; x, <span class="keyword">const</span> AutoDiffScalar&lt;DerType&gt;&amp; y) {</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  <span class="keywordflow">return</span> (x.value() &gt;= y.value() ? x : y);</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;}</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160; </div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>,</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(x.value()), x.derivatives() * (x.value()&lt;0 ? -1 : 1) );)</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160; </div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a>,</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;  <span class="keyword">using</span> numext::abs2;</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a>(x.value()), x.derivatives() * (Scalar(2)*x.value()));)</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160; </div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>,</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;  Scalar sqrtx = <a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(x.value());</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>,</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;  <span class="keyword">using</span> std::cos;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="keyword">using</span> std::sin;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(x.value()), x.derivatives() * (-<a class="codeRef" href="../namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>(x.value())));)</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160; </div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>,</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  <span class="keyword">using</span> std::sin;</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;  <span class="keyword">using</span> std::cos;</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>(x.value()),x.derivatives() * <a class="codeRef" href="../namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(x.value()));)</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160; </div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>,</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;  <span class="keyword">using</span> std::exp;</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;  Scalar expx = <a class="codeRef" href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(x.value());</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(expx,x.derivatives() * expx);)</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160; </div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>,</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(x.value()),x.derivatives() * (Scalar(1)/x.value()));)</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160; </div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;template&lt;typename DerType&gt;</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;<span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">Eigen::AutoDiffScalar</a>&lt;</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t&lt;DerType&gt;, <span class="keyword">typename</span> internal::traits&lt;internal::remove_all_t&lt;DerType&gt;&gt;::Scalar,product) &gt;</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;pow(<span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">Eigen::AutoDiffScalar&lt;DerType&gt;</a> &amp;x, <span class="keyword">const</span> <span class="keyword">typename</span> internal::traits&lt;internal::remove_all_t&lt;DerType&gt;&gt;::Scalar &amp;y)</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;{</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  <span class="keyword">using namespace </span><a class="code" href="namespaceEigen.html">Eigen</a>;</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(pow(x.value(),y), x.derivatives() * (y * pow(x.value(),y-1)));</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;}</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160; </div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160; </div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> DerTypeA,<span class="keyword">typename</span> DerTypeB&gt;</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;<span class="keyword">inline</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;Matrix&lt;typename internal::traits&lt;internal::remove_all_t&lt;DerTypeA&gt;</a>&gt;::Scalar,<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>,1&gt; &gt;</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;atan2(<span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;DerTypeA&gt;</a>&amp; a, <span class="keyword">const</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;DerTypeB&gt;</a>&amp; b)</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;{</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="keyword">using</span> std::atan2;</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits&lt;internal::remove_all_t&lt;DerTypeA&gt;&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;Matrix&lt;Scalar,Dynamic,1&gt;</a> &gt; PlainADS;</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  PlainADS ret;</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;  ret.value() = atan2(a.value(), b.value());</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;  </div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;  Scalar squared_hypot = a.value() * a.value() + b.value() * b.value();</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;  </div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;  <span class="comment">// if (squared_hypot==0) the derivation is undefined and the following results in a NaN:</span></div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;  ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot;</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160; </div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;}</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160; </div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">tan</a>,</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;  <span class="keyword">using</span> std::tan;</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;  <span class="keyword">using</span> std::cos;</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">tan</a>(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(<a class="codeRef" href="../namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(x.value()))));)</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160; </div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">asin</a>,</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;  <span class="keyword">using</span> std::asin;</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">asin</a>(x.value()),x.derivatives() * (Scalar(1)/<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(1-numext::abs2(x.value()))));)</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;  </div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">acos</a>,</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keyword">using</span> std::acos;</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">acos</a>(x.value()),x.derivatives() * (Scalar(-1)/<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(1-numext::abs2(x.value()))));)</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160; </div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">tanh</a>,</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;  <span class="keyword">using</span> std::cosh;</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;  <span class="keyword">using</span> std::tanh;</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">tanh</a>(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(<a class="codeRef" href="../namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">cosh</a>(x.value()))));)</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160; </div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>,</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;  <span class="keyword">using</span> std::sinh;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  <span class="keyword">using</span> std::cosh;</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>(x.value()),x.derivatives() * <a class="codeRef" href="../namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">cosh</a>(x.value()));)</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160; </div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(<a class="codeRef" href="../namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">cosh</a>,</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;  <span class="keyword">using</span> std::sinh;</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;  <span class="keyword">using</span> std::cosh;</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;  <span class="keywordflow">return</span> Eigen::MakeAutoDiffScalar(<a class="codeRef" href="../namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">cosh</a>(x.value()),x.derivatives() * <a class="codeRef" href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>(x.value()));)</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160; </div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160; </div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;template&lt;typename DerType&gt; <span class="keyword">struct</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits</a>&lt;<a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;DerType&gt;</a> &gt;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;  : <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits</a>&lt; <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits</a>&lt;<span class="keyword">typename</span> internal::remove_all_t&lt;DerType&gt;::Scalar&gt;::Real &gt;</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;{</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;  <span class="keyword">typedef</span> internal::remove_all_t&lt;DerType&gt; DerTypeCleaned;</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;Matrix&lt;typename NumTraits&lt;typename DerTypeCleaned::Scalar&gt;::Real</a>,DerTypeCleaned::RowsAtCompileTime,DerTypeCleaned::ColsAtCompileTime,</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;                                0, DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime&gt; &gt; Real;</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;DerType&gt;</a> NonInteger;</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar&lt;DerType&gt;</a> Nested;</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;typename DerTypeCleaned::Scalar&gt;::Literal</a> Literal;</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;  <span class="keyword">enum</span>{</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;    RequireInitialization = 1</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;  };</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;};</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160; </div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;}</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160; </div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;<span class="keyword">namespace </span>std {</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160; </div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;<span class="keyword">class </span>numeric_limits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::<a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar</a>&lt;T&gt; &gt;</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;  : <span class="keyword">public</span> numeric_limits&lt;typename T::Scalar&gt; {};</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160; </div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;<span class="keyword">class </span>numeric_limits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::<a class="code" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar</a>&lt;T&amp;&gt; &gt;</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;  : <span class="keyword">public</span> numeric_limits&lt;typename T::Scalar&gt; {};</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160; </div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;}  <span class="comment">// namespace std</span></div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160; </div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_AUTODIFF_SCALAR_H</span></div>
<div class="ttc" id="aclassEigen_1_1AutoDiffScalar_html"><div class="ttname"><a href="classEigen_1_1AutoDiffScalar.html">Eigen::AutoDiffScalar</a></div><div class="ttdoc">A scalar type replacement with automatic differentiation capability.</div><div class="ttdef"><b>Definition:</b> AutoDiffScalar.h:73</div></div>
<div class="ttc" id="aclassEigen_1_1AutoDiffScalar_html_a0c41ac30584453395197d74637919aef"><div class="ttname"><a href="classEigen_1_1AutoDiffScalar.html#a0c41ac30584453395197d74637919aef">Eigen::AutoDiffScalar::AutoDiffScalar</a></div><div class="ttdeci">AutoDiffScalar()</div><div class="ttdef"><b>Definition:</b> AutoDiffScalar.h:86</div></div>
<div class="ttc" id="aclassEigen_1_1AutoDiffScalar_html_ac495df4f841747d994c15970804b0f55"><div class="ttname"><a href="classEigen_1_1AutoDiffScalar.html#ac495df4f841747d994c15970804b0f55">Eigen::AutoDiffScalar::AutoDiffScalar</a></div><div class="ttdeci">AutoDiffScalar(const Scalar &amp;value, int nbDer, int derNumber)</div><div class="ttdef"><b>Definition:</b> AutoDiffScalar.h:90</div></div>
<div class="ttc" id="aclassEigen_1_1AutoDiffScalar_html_adbf812d694d82049f27b55fbd6c1fb50"><div class="ttname"><a href="classEigen_1_1AutoDiffScalar.html#adbf812d694d82049f27b55fbd6c1fb50">Eigen::AutoDiffScalar::AutoDiffScalar</a></div><div class="ttdeci">AutoDiffScalar(const Real &amp;value)</div><div class="ttdef"><b>Definition:</b> AutoDiffScalar.h:98</div></div>
<div class="ttc" id="aclassEigen_1_1AutoDiffScalar_html_ae6483e33249241b62b9f2506faaf8bbf"><div class="ttname"><a href="classEigen_1_1AutoDiffScalar.html#ae6483e33249241b62b9f2506faaf8bbf">Eigen::AutoDiffScalar::AutoDiffScalar</a></div><div class="ttdeci">AutoDiffScalar(const Scalar &amp;value, const DerType &amp;der)</div><div class="ttdef"><b>Definition:</b> AutoDiffScalar.h:106</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a0110c233d357169fd58fdf5656992a98"><div class="ttname"><a href="../namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">Eigen::tanh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tanh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tanh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a04d60a3c8a266f63c08e03615c1985c9"><div class="ttname"><a href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">Eigen::imag</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_imag_op&lt; typename Derived::Scalar &gt;, const Derived &gt; imag(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a34b99a26a2a1e7ff985a5ace16eedfcb"><div class="ttname"><a href="../namespaceEigen.html#a34b99a26a2a1e7ff985a5ace16eedfcb">Eigen::cosh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cosh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cosh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3bc116a6243f38c22f851581aa7b521a"><div class="ttname"><a href="../namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">Eigen::tan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3fe3a136370fefae062591304c6a7ebd"><div class="ttname"><a href="../namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">Eigen::acos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_acos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; acos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a54cc34b64b4935307efc06d56cd531df"><div class="ttname"><a href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">Eigen::abs2</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs2_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs2(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a6c5c246b877ac331495d21e7a5d51616"><div class="ttname"><a href="../namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">Eigen::asin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_asin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; asin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ab84f39a06a18e1ebb23f8be80345b79d"><div class="ttname"><a href="../namespaceEigen.html#ab84f39a06a18e1ebb23f8be80345b79d">Eigen::conj</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_conjugate_op&lt; typename Derived::Scalar &gt;, const Derived &gt; conj(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ac74dc920119b1eba45e9218d9f402afc"><div class="ttname"><a href="../namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">Eigen::real</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_real_op&lt; typename Derived::Scalar &gt;, const Derived &gt; real(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad01d50a42869218f1d54af13f71517a6"><div class="ttname"><a href="../namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">Eigen::cos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad225313de8037d40c2d26c17edf1a9fd"><div class="ttname"><a href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; Inverse&lt; PermutationType &gt;, SparseDerived, AliasFreeProduct &gt; operator*(const InverseImpl&lt; PermutationType, PermutationStorage &gt; &amp;tperm, const SparseMatrixBase&lt; SparseDerived &gt; &amp;matrix)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae491aecf7dab66ac7e11008c5766694d"><div class="ttname"><a href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">Eigen::exp</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_exp_op&lt; typename Derived::Scalar &gt;, const Derived &gt; exp(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae6e8ad270ff41c088d7651567594f796"><div class="ttname"><a href="../namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">Eigen::sin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae8bb75ba4f5f30a7571146dbfa653c6d"><div class="ttname"><a href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">Eigen::log</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af284ce359b6efd4b594a9f8a1f5e5d96"><div class="ttname"><a href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">Eigen::sinh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sinh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sinh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="../structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div></div>
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